Earlier quoted context omitted.
Is this your opinion or is this something that’s an actual theory in sociology or psychology, or at least something people talk about in practice? Not trying to be mean, just to learn. There’s a whole genre of press releases and videos for apologies, so I’m not sure it’s such a reputational risk to admit one is wrong. It might be a bigger risk not to, it would seem. But what you say sounds interesting.
I would be interested too if that's an actual theory. My experience has largely been that if you're willing to admit you were wrong about something, most reasonable people will appreciate it over you doubling down. If they pile on after you have conceded, typically they come off much worse socially in my opinion.
Admitting the mistake in front of strangers, usually leads to them making the shortcut next time and assuming you are wrong again.
you wont get any awards for admitting the mistake.